Applied Econometrics and International Development Vol- 8-2 (2008)

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1 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) HEALTH, EDUCATION AND ECONOMIC GROWTH: TESTING FOR LONG- RUN RELATIONSHIPS AND CAUSAL LINKS AKA, Béda F. * DUMONT, Jean Chrsophe Absrac Ths paper examnes he causal relaonshps beween human capal (Educaon, and Healh) and Economc growh (GDP per capa) for he USA usng me seres approach. We fnd conegraon beween he seres under sudy meanng ha he varables have long-run relaonshps. The EC-VAR nvesgaons show b-dreconal causaly beween human capal varables and growh. Gven he b-dreconal causaon, we perform varance decomposon and mpulse response funcons o see he mporance of he mpacs among hese varables. The resuls show ha he long-run dynamcs of economc growh can be explaned by pas educaon level whle a lesser par of hese varaons are relaed o healh level. In he long-run horzon educaon shocks are mporan a explanng healh level, alhough growh shocks accoun for abou more han one-hrd of healh. Economc growh accouns for more par n he explanaon of educaon level. JEL Classfcaon: C32; I; I2 Keywords: Human Capal, Healh, Educaon, Economc growh, Conegraon, ECM, Causaly.. Inroducon Ths paper emprcally examnes he long-run relaonshps and he causal lnks beween educaon (E), healh (H) and economc growh (G). Ths queson has been wdely nvesgaed by many auhors wh dverse success. Especally, posve and sgnfcan relaonshp beween educaon and economc growh s rarely found n panel daa analyses [see e.g. Barro and Lee - 993, Barro - 994, Benhabb and Spegel - 994, Islam - 995] whch conradcs prevous fndngs n cross secon analyses [see e.g. Landau - 986, Barro - 99, Mankw, Romer and Wel - 992]. In he same ven, he lnk beween economc growh and healh, somemes observed n cross counry analyses [see e.g. Landau - 986, Sachs and Warner - 997], appears o be poenally spurous [see Barro and Lee - 993]. Besdes daa qualy problems, hs leraure suffers from dfferen ypes of echncal and concepual shorcomngs. Le us pon ou wo of hem. () Almos every sudy looks a one-o-one relaonshp. However f one beleves ha human capal major componens (.e. educaon and healh) are no perfec subsues * Béda F. Aka, Deparmen of Economcs and Lampe (Laboraory of analyss modellng and economc perspecve), Unversy of Bouaké, Côe d'ivore, Emal: akbda@yahoo.fr, and Jean- Chrsophe Dumon, OECD, Pars. Prncpal Admnsraor, Drecorae of Employmen, Labour and Socal Affars, Non-member Economes and Inernaonal Mgraon Dvson, Emal: jeanchrsophe.dumon@oecd.org Acknowledgemen: We are very graeful for he commens and addonal daa from he edor. Ths paper was sared when he auhors were vsng research fellow a Unversy of Laval, Québec, Canada. The auhors would lke o hank AUF and CREFA (Deparmen of Economcs, Unversy of Laval). Useful commens from an anonymous referee are graefully acknowledged.

2 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) and nerac, seems necessary o consder her connecon o economc growh whn a jon model. Schulz (997) srongly advocaes for such a developmen: 'Inegraed analyss of hese varous forms of human capal s now needed o measure wh greaer precson each of her effecs on economc developmen'. () Wh some very few excepon [see e.g. de-meulemeeser and Rocha - 995], emprcal works rely on regresson mehod (panel of cross secon) nsead of causaly echnques. The weakness of hese sudes s o adequae correlaon wh causaon. Bu s well known ha wo varables may be hghly correlaed bu no necessarly causally lnked [Lükepohl - 99]. In hs paper we offer o develop an economerc me seres analyss, where economc growh, educaon and healh are consdered smulaneously. To acheve hs objecve he mehodology used reles on a r-varae EC-VAR model. We explcly es for conegraon n he consrucon of he causaly ess. The model s esed on he me seres daa for he US over he perod The oulne of he paper s as follow. Secon 2 presens he economerc mehodology. Secon 3 presens he emprcal resuls ncludng conegraon and causaly analyses, varance decomposon and mpulse response funcons. Concludng remarks are gven n secon Conegraon and Error Correcon Model Pror o es for conegraon and causaly, un roo ess are performed on each varable o deermne he order of negraon. The ADF es s used o check for un roo and saonary, and s conduced from he esmaon of he followng equaons: E H G p + ρ E + ρ + φk E ε () 0 2 = ρ + p + ρ H + ρ + φk H ε (2) 0 2 = ρ + p + ρ G + ρ + φk G ε (3) 0 2 = ρ + where s he frs dfference operaor, ε s a whe nose error erm, s a me rend, and p s chosen such ha he resduals are serally uncorrelaed. The null hypohess of non saonary s rejeced f ρ 0 and sascally sgnfcan, [see Macknnon -99]. < The Johansen (988) and Johansen and Juselus (990) mulvarae mehodology o es for conegraon based on he vecor auoregressve (VAR) sysem of n x vecor varables X s used: X = µ + Γ + X Γp X p + ε (4) Wheller (980) s one of he very few o esmae a smulaneous model where educaon, healh, nuronal saus, populaon growh and economc growh are jonly deermne. The resuls seem o valdae he exsence of muldmensonal relaonshps across hose facors bu has no been confrmed snce. 02

3 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. where X =[E,H,G ]', wh E,H,G represenng educaon, healh and economc growh E H G respecvely, ε = [ ε, ε, ε ]' ndcang srucural shocks of educaon, healh and growh. Johansen and Juselus (990), usng maxmum lkelhood, have developed wo sascs o es he null of no conegraon. These sascs are he Trace sasc and he maxmal egenvalue sasc (Max-L), and compued as follow: Trace = T N r+ ln( λ ) (5) Max L = T ln( λ r+ ) (6) where r s he number of conegraon vecors and λ...λ N are he N square canoncal correlaons beween X -p and X, he seres beng ranged n a decreasng order so ha λ > for >j. Crcal values are n Oserwald-Lenum (992). If he compued λ j sascs s lower han he crcal value, one can rejec he null hypohess of no conegraon. The conegraon analyss developed by Johansen ess he hypohess ha wo varables have no equlbrum condon keepng hem n proporon o each oher n he long run. The lack of long run relaonshp provdes evdence ha he varables are no conegraed. In causaly analyss, where no conegraon s found, classcal Granger causaly ess old. Bu f he seres are conegraed hen s approprae o re-parameerze he model n he equvalen error correcon model (ECM) form, oherwse nference may be nvald as he esmaes may suffer from he spurous regresson problem, n such a case causaly esng can lead o erroneous conclusons. Furhermore, ECM-based causaly ess offer he addonal advanage ha he source of causaon can be denfed, n he form of eher shor-run dynamcs or dsequlbrum adjusmen. The followng ree-varables ECM can be used o es for Granger causaly [see Granger, 963; 969; 988; Hendry e al., 984; Engle and Granger, 987; Johansen, 988]: n a mulvarae case based on he regressons: s q q E = Ω0 + Ω E + Ω2 H + Ω3 G +δ µ + ε (7) s q q H = Ω20 + Ω2 E + Ω22 H + Ω23 G +δ 2η + ε2 (8) s q q G = Ω30 + Ω3 E + Ω32 H + Ω33 G +δ 3θ + ε3 (9) where E, H and G are dfference saonary and conegraed wh µ, η and θ represenng he lagged values of he error erms from conegrang regressons. The random errors are gven by ε, ε 2 and ε 3, and capure all shor-run devaon from H o E, from E o H and from H o G, s and q are deermned by Akake nformaon creron (AIC). 03

4 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) Under he null hypohess of non causaly beween H and E gven G, H 0 ( Ω =Ω2 =Ω3 = δ = 0, Ω2 =Ω22 =Ω23 = δ2 = 0 and Ω3 =Ω32 =Ω33 = δ3 = 0). A sraghforward F-es can be used o es H 0. A feedback relaonshp beween H and E n he presence of oher facor (G) requres ha he coeffcens Ω Ω, Ω, Ω 2, Ω 22, Ω 23 and 2 δ are jonly sgnfcan., 2 3 δ The lagged changes n he ndependen varable n equaon 7, 8 and 9 can be nerpreed as represenng he shor-run causal mpac, whle he error erms provde he adjusmen of E, H and G owards her respecve long-run equlbrum. In addon o he sandard sasc of he coeffcen on a group of lagged varables repored n Granger causaly ess, examnaon of he sasc on he respecve error correcon erm can also lead o nfer causaly. For example, from equaon 7, a sascally sgnfcan coeffcen for µ, suggess ha H causes E. Lkewse from Equaon 8, a sascally sgnfcan coeffcen on η suggess ha E causes H. If he boh error correcon erms from Equaons 7 and 8 are sascally sgnfcan hen b-dreconal causaly (or feedback) exss. When bdreconal causaly s found, varance decomposon has o be performed o shed lgh on he double causaly. In he causaly es proposed by Granger (969), consderng he null hypohess ha he coeffcens of lagged values of he educaon and healh varables are no sascally sgnfcan n equaon (9), he es s a sandard ch- square es. As he dependen varable s he GDP per capa growh rae, we are hus esng f here s a drec mpac of educaon or healh on growh. Ths paper performs causaly es beween educaon, healh, and economc growh usng he ECM represenaon n case conegraon was found. 3. Evdence from Conegraon and Causaly Tess The causaly hypohess s now esed usng yearly USA daa from dfferen sources coverng he perod We consder a flow varable for educaon, namely he number of hgh school graduaed (publc and prvae) 2. The naural logarhm of he number of graduae sudens as educaon seres are from Clauda Goldn (999) and NCES (993). Economc growh s compued as he gross domesc produc n chaned 992 bllon dollars (source NIPA). Healh condons are proxes by he esmaed average lengh of lfe a brh (Naonal val sascs repor, volume 47 n 3, 993, NCHS). Populaon daa are from Naonal Populaon Esmaes (US Bureau of Census). The seres are presened n Table, and n able A of he Annex, and Fgure shows he 3 varables n log level (Top panel), frs dfference (mddle panel) and second dfference (boom panel) over he perod of sudy. 2 A sock varable represened by years of school compleed by he persons 25 years and over had been also consdered. However, as s avalable from 950, we kep he former ndcaor. 04

5 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. Table. Daa of Educaon, Healh, GDP, Populaon and Consumpon Prce Index: fve-year daa of he perod Year Educaon Healh GDP curren prces GDP consan 990 prces Populaon GDP p.c. consan CPI Noe: Annual daa for n able A of he Annex. GDP per capa (p.c.) n housand dollars per nhaban a 990 prces. Sources: See foonoe n able A. Fgure. Educaon, Healh and Growh n log level, frs dfference and second dfference LEDUC 4.3 LHEALTH 3.0 LY DLEDUC DDLEDUC DLHEALTH DDLHEALTH DLY DDLY

6 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) The prelmnary sep n our emprcal sudy s concerned wh he degree of negraon or he saonary of each varable n he VAR sysem. The varables have been esed for un roo usng he Dckey-Fuller procedure [see Dckey and Fuller, -98]. The resuls (no repored here) ndcae ha he 3 varables are I(2) processes (see Fgure boom panel). Gven he resuls of he un roo es, s possble o es for he exsence of a sable relaonshp beween healh, educaon and economc growh. Based on Akake nformaon creron (AIC), we fnd ha 9 lags are he bes o represen he dynamc srucure of he VAR sysem 3. The Johansen es for conegraon ndcaes 2 conegrang relaonshps beween he varables [see Table 2]. Tha means long-run relaonshps exs beween he 3 varables. Gven he resuls from he conegraon es an EC-VAR model s approprae n he causaly analyses. Table 2. Johansen Conegraon Tess for Educaon, Healh and Economc Growh I() conegraon analyss, 940 o 996 Egenvalue log-lkelhood for rank H0:rank<= Trace es [ Prob] [00] ** [00] ** [0.235] Concluson 2 Conegraon relaons Noe: ** denoes rejecon of he null hypohess. Causaly Analyses In Table 3 we repor he es sascs for emporal causaly beween he varables. To deermne he drecon of causaly beween he dependan and he ndependen varables (+ or relaonshps), he sgn of he sum of coeffcen of lagged values of he causal facor s repored, he null hypohess beng non-causaon. Table 3. ECM Causaly Tess Resuls for Educaon, Healh and Economc Growh Causal Inference EC Term Ch^2-sa Sgn of Causaon Lag lengh E G [0.6652] [20]* + 9 G E [000]** 40.8 [000]** + 9 H G [0.6652] [20]* - 9 G H [000]** [000]** - 9 H E [000]** 40.8 [000]** + 9 E H [000]** [000]** + 9 Noe: * denoes rejecon of he null hypohess. 3 We sared wh he maxmum lag se a 20, whle he mnmum a. 06

7 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. We fnd causaly from healh o educaon and vce versa (H E). We also fnd ha pas healh levels mpac economc growh (H G) as well as beween educaon and growh (E G). Varance Decomposon The varance decomposon allows a beer undersandng of he double causaly beween he varables. Varance decomposon 4 shows he conrbuon of each source of nnovaon o he varance of k-year ahead forecas error for each of he varables ncluded n he sysem. In oher words, varance decomposons show how much of he forecas error varance for each endogenous varable can be explaned by each dsurbance. As hs decomposon s no unque, gven he resuls of hs causaly ess, he varables are ordered by consderng he case where he assocaed F-sascs were hgher. The resuls of hese nvesgaons are shown n Table 4. Table 4. Varance Decomposon for Human Capal and Economc Growh Horzon Impulse response o DDLY (un mpulse) GROWTH EDUC HEALTH Orderng: Growh Educaon- Healh Impulse response o DDLEDUC (un mpulse) GROWTH EDUC HEALTH Impulse response o DDLHEALTH (un mpulse) GROWTH EDUC HEALTH () The varaon of economc growh A perod 0, 2.48% of he varaon of economc growh s explaned by pas healh level and 97.60% by pas educaon level, whle 9.5% by pas economc growh rae. The varaon of economc growh rae can be explaned by pas educaon level n he long-run whle a slgh par of hese varaons are relaed o healh level. () The varaon of educaon level A perod 0, 8.84% of pas healh levels explan he varaon of educaon and 4.3% of pas educaon levels explan he same varaon, whle 76.29% of pas 4 Ths calculaon s acheved by orhogonalzaon of he nnovaons usng he Cholesk decomposon mehod (Doan, 992). Ths decomposon depends on he order whch he varables ener he VAR sysem. 07

8 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) economc growh raes explan he varaon of educaon. In he long-run horzon, economc growh accoun for more par n he explanaon of educaon level. () The varaon of healh level A perod 0, 685.2% of he varaon of healh s explaned by pas healh level, 344.% by pas educaon level and 366.5% by pas economc growh rae. Tha means educaon shocks are mporan for explanng healh level n he long-run, alhough growh shocks accoun for abou more han one-hrd. Impulse Response Funcons Impulse response ndcaes he dynamc effecs of a shock of one varable on he oher one, as well as on he varable self. Fgure 2 shows he mpulse response funcons, whch are he respond of he 3 varables o each shock over a en-year horzon (we use accumulaed orhogonalzed mpulse response). In he long run, an mpulse o he human capal and growh varables ncreases he GDP per capa (Top panel), educaon (mddle panel) and healh (boom panel). These are perods when response funcons are above he baselne more han compensae for perods below. In ne erms, human capal formaon nduces economc growh. The accumulaed effec on growh derved from an mpulse on human capal s greaer han zero, as can be read from Table 4. Fgure 2. Accumulaed Impulse Response (orhogonalzed mpulse) cum DDLY (DDLY eqn) cum DDLY (DDLEDUC eqn) cum DDLEDUC (DDLY eqn) cum DDLEDUC (DDLEDUC eqn) cum DDLHEALTH (DDLY eqn) cum DDLHEALTH (DDLEDUC eqn) cum DDLY (DDLHEALTH eqn) 0 cum DDLEDUC (DDLHEALTH eqn) 2.5 cum DDLHEALTH (DDLHEALTH eqn) Noes: DDLHEALTHeqn ndcaes Healh Response (Boom panel), DDLEDUCeqn ndcaes Educaon Response (Mddle panel) and DDLYeqn ndcaes Economc Growh Equaon (Top panel). 08

9 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. 4. Concludng Remarks In hs paper, we re-examne he long-run relaonshps and causaly beween educaon, healh and economc growh n USA, usng an economerc me seres approach. We fnd conegraon beween he 3 varables ndcang a long-run relaonshp beween economc growh, healh and educaon. We also fnd usng ECM mehodology bdreconal causaly beween he suded varables. Gven hs b-dreconal causaly beween he varables, we conduced varance decomposon and mpulse response funcons o hghlgh he proporon of he effec of one varable on he oher. Our emprcal evdence shows ha he long-run dynamcs of he growh process are explaned by pas healh and educaon level. Fuure research should address hese relaonshps and causal lnks for oher ndusralzed counres and for developng counres as well o emphasze he role of human capal on economc growh. References Barro, R. (99) Economc growh n a cross secon of counres, Quarerly Journal of Economcs, 06(2), Barro, R. and Lee, J-W. (993) Inernaonal comparsons of educaonal aanmen, Journal of Moneary Economcs, 32(3), Benhabb, J. and Spegel, M. (994) The role of human capal n economc developmen: evdence from cross-counry daa, Journal of Moneary Economcs, 34, Goldn, C. (999) A Bref Hsory of Educaon n he Uned Saes, NBER Hsorcal Paper No. 9, Augus 999. DeMeulemeeser, J. and Rocha, D. (995) A causaly analyss of he lnk beween hgher educaon and economc developmen, Economcs of Educaon Revew, 4 (4), Dckey, D. and Fuller, W. (979) Dsrbuon of he esmaors for auoregressve me seres wh a un roo, Journal of he Amercan Sascal Assocaon, 74, Engle, R.F. and Granger, C.W.J. (987) Conegraon and error correcon: represenaon, esmaon and esng, Economerca, 55, Granger, C.W.J. (963) Processes nvolvng feedback, Informaon and Conrol, 6, Granger, C.W.J. (969) Invesgang Causal Relaons by Economerc Models and Cross-Specral Mehods, Economerca, 37, Granger, C.W.J. (986) Developmens n he sudy of conegraed economc varables, Oxford Bullen of Economcs and Sascs, 48, Granger, C.W.J. (988) Causaly, Conegraon, and Conrol, Journal of Economc Dynamcs and Conrol, 2, Granger, C.W.J. (988) Some recen developmens n a concep of causaly, Journal of Economercs, 39,

10 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) Hendry, D. F., Pagan, A. R., and Sargan, J. D. (984) Dynamc specfcaon, n Grlches, & Inrlgaor (984), Ch. 8.Reprned n Hendry, D. F., Economercs: Alchemy or Scence? Oxford: Blackwell Publshers, 993, and Oxford Unversy Press, Islam, N. (995) Growh emprcs: a panel daa approach, Quarerly Journal of Economcs, vol. 0(95), Islam, M.W. (998) Expor expanson and economc growh: esng for conegraon and causaly, Appled Economcs, 30, Johansen, S. (988) Sascal analyss of Conegraon vecors, Journal of Economc Dynamcs and Conrol, 2, Johansen, S. and Juselus, K. (990) Maxmum Lkelhood Esmaon and nference on Conegraon - wh applcaons o he Demand for money, Oxford Bullen of Economcs and Sascs, 52, Landau, D. (986) Governmen Expendure and Economc Growh n he Less Developed Counres, an Emprcal Sudy for Economc Developmen & Culural Change, Lükepohl, H. (99) Inroducon o mulple me seres analyss, Sprnger-Verlag, Berln. MacKnnon, J. J. (99) Crcal values for conegraon ess, n Readngs n conegraon (Ed) R.F. Engle and Granger, C.W. Oxford Unversy Press, Oxford, pp Mankw, N.G., D. Romer and D.N. Wel. (992) A conrbuon o he emprcs of economc growh, Quarerly Journal of Economcs, 07(2), Oserwald-Lenum, M. (992) A Noe wh Quanles of he Asympoc Dsrbuon of he Maxmum Lkelhood Conegraon Rank Tes Sascs, Oxford Bullen of Economcs and Sascs, 54, Payne, J.E. and Ewng, B.T. (997) Populaon and economc growh: a conegraon analyss of lesser developed counres, Appled Economc Leers, 4, Sachs, J.D. and Warner, A. (997) Fundamenal sources of long-run growh, Amercan Economc Revew, Papers and Proceedngs 87, 2, Schulz, T.P. (997) Assessng he Producve Benefs of Nuron and Healh: An Inegraed Human Capal Approach, Journal of Economercs, 77, Wheller, D. (980) Basc needs fulflmen and economc growh: a smulaneous model, Journal of Developmen Economcs, 7, On lne Annex a he journal webse: hp:// 0

11 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. Annex Table A: Human Capal and Economc Growh YEAR EDUCATION HEALTH GDP POPULATION IPC90U ,

12 Appled Economercs and Inernaonal Developmen Vol- 8-2 (2008) Table : Human Capal and Economc Growh (connue) YEAR EDUCATION HEALTH GDP POPULATION IPC90U

13 Aka, B.F., Dumon, J.C. Healh, Educaon and Economc Growh. Tesng Causal Lnks n The U.S. Noes o able : - Educaon: number of Hgh school graduaes, by sex and conrol of nsuon: o 99 92, Graduaes per 00, 7-year-olds (publc and prvae). The naural logarhm of he number of graduae sudens as educaon seres are from Clauda Goldn (999) and NCES (993). 2- Healh: proxes by he esmaed average lengh of lfe n years, by race and sex: Deahregsraon Saes, , and Uned Saes, (Naonal val sascs repor, volume 47 n 3, December 24, 998, NCHS). hp:// 3- GDP: Economc growh: compued as he gross domesc produc n chaned 992 bllon dollars (source NIPA), hp:// and hp:// 4- Populaon: Hsorcal Naonal Populaon Esmaes: July, 900 o July, 999: Populaon Esmaes Program, Populaon Dvson, U.S. Census Bureau; Inerne Release Dae: Aprl, 2000; revsed dae: June 28, Naonal populaon daa for he years 900 o 949 exclude he populaon resdng n Alaska and Hawa. Naonal populaon daa for he years 940 o 979 cover he resden populaon plus Armed Forces overseas. Naonal populaon daa for all oher years cover only he resden populaon. Esmaes of he populaon ncludng Armed Forces overseas are as follows: 99: 05,063,000; 98: 04,550,000; 97: 03,44,000. Naonal populaon daa for he years 900 o 929 are only avalable rounded o he neares housand. Daa for hs able comes from Curren Populaon Repors, Seres P-25, Nos. 3, 97, 095, and Naonal Populaon Esmaes web page. hp:// 5- IPC90U: Prce ndex of Prvae Consumpon of he USA, base 990 (IPC90u= n 990) The GDP per capa X s dvded by he Prce ndex gvng: Y=X/Ipc90u. 3